Question

which statements about the measures of center are true? select three choices. the mean for group a is less than the mean for group b. the median for group a is less than the median for group b. the mode for group a is less than the mode for group b. the median for group a is 2. the median for group b is 3.

Explanation:

First, we define the two groups from the dot plot:

• Group A: Values at 1,1,1,2,2 (3 dots at 1, 2 dots at 2)
• Group B: Values at 3,3,3,5 (3 dots at 3, 1 dot at 5)

Step1: Calculate Group A mean

$\text{Mean}_A = \frac{1+1+1+2+2}{5} = \frac{7}{5} = 1.4$

Step2: Calculate Group B mean

$\text{Mean}_B = \frac{3+3+3+5}{4} = \frac{14}{4} = 3.5$

Step3: Find Group A median

Order Group A: [1,1,1,2,2]. Middle value is 1.

Step4: Find Group B median

Order Group B: [3,3,3,5]. Middle values are 3 and 3, so median = $\frac{3+3}{2}=3$

Step5: Find Group A mode

Most frequent value in Group A is 1.

Step6: Find Group B mode

Most frequent value in Group B is 3.

Step7: Verify each statement

1. $\text{Mean}_A=1.4 < \text{Mean}_B=3.5$: True
2. $\text{Median}_A=1 < \text{Median}_B=3$: True
3. $\text{Mode}_A=1 < \text{Mode}_B=3$: True
4. Median for Group A is 2: False
5. Median for Group B is 3: True

We need to select three true statements, and the first three verified statements are valid, along with the fifth, but we select the three clear correct ones as required.

Answer:

A. The mean for Group A is less than the mean for Group B.
B. The median for Group A is less than the median for Group B.
C. The mode for Group A is less than the mode for Group B.